Enable Signup with Google Auth

I am using Project Invitation plugin to invite users to a project. The users receives a signup link that doesn’t provide any option to signup/register using Google auth.

Ideally, if the Google Auth plugin is installed and configured, it should provide an option to signup via Google Auth.

I have also noticed that if I login through Google and send an invite to the same email address, the invite gets sent and the same user can register with a different username and the same email address.